An analytic model for nonlinear propagation theory is developed for multi-wavelength laser beams propagating in an isotropic media. The small-scale self-focusing theoretical solution of multi-wavelength beams is obtained and is superposed by eigenfunctions with multiple local fastest-growth frequency, so the traditional B-integral obtained from a single-wavelength beam cannot be used to describe the small-scale self-focusing of multi-wavelength beams. Some laws for multi-wavelength beams propagating in an isotropy medium are also found, such as the self-focusing distance decreasing, the large angle scattering increasing and the spatial distributions of each wavelength trending to be consistent. The theoretical laws are confirmed by integrated numerical simulations and provide an explanation for the final optics phenomenon in high power lasers. The results promote the understanding of self-focusing theory and provide a very promising tool for beam control, which can transfer info...

中文翻译：

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各向同性介质中多波长光束小尺度自聚焦的理论分析

针对各向同性介质中传播的多波长激光束，建立了非线性传播理论的解析模型。由于获得了多波长光束的小尺度自聚焦理论解，并与具有多个局部最快增长频率的本征函数叠加，所以不能使用从单波长光束获得的传统B积分来描述小波长光束。缩放多波长光束的自聚焦。还发现了在各向同性介质中传播的多波长光束的一些定律，例如自聚焦距离减小，大角度散射增大以及每个波长的空间分布趋于一致。理论定律已通过集成数值模拟得到了证实，并为大功率激光器中的最终光学现象提供了解释。